It's only potentially unsafe if you have switched off the default action of Thunderbird to not allow remote content to display or if you have changed the default and selected 'Display Attachments Inline' or you click on links in an opened email without checking whether the link is legit before clicking on it or opening attachments that are clearly bogus.

However, I notice someone else has reported an issue with downloading when they also only downloaded the headers, so I'll see if I can find out a bit more on that.

Are you talking about a gmail account ?

Did you try to see if this was due to your 'Disc Space' settings? For example: do not download messages larger than xx kb.

Another person seems to have same issue, so providing a link just in case info needs to be shared. https://support.mozilla.org/en-US/questions/1158714#answer-964685

I have two accounts in the profile. None of them is gmail. Both demonstrate the same problem. I have no limit set for disk space.

https://support.mozilla.org/en-US/questions/1158546

TB 52.0.1 available here.

Workaround

Had to go back to 52.0.1 because 52.1.0 Fetch Headers Only (pop); messages will not load. Everything fine. Now, 52.1 just updated automatically against my choices & again messages will not load.

52.1.1 is up